Soliton diffusion in polyacetylene. II. Acoustic phonons

The soliton diffusion due to the coupling to acoustic phonons in polyacetylene is analyzed theoretically within the Su, Schrieffer, and Heeger model. It is shown that in the temperature region $T\ll \frac{1}{2}{\omega }_0$, where ${\omega }_0$ (∼2000 K) is the optical-phonon frequency, the acoustic phonon dominates the soliton damping. Furthermore, for $T\gg T_0$, the single-phonon process dominates the soliton diffusion where $T_0=2m{c}^2$, and $m$ and $c$ are the soliton mass and the acoustic-phonon velocity, respectively. The one-dimensional model predicts the temperature-dependent diffusion constant $D\propto T^{\frac{1}{2}}$, while the three-dimensional model predicts $D\propto T^{-\frac{1}{2}}$. The latter temperature dependence appears to be consistent with some of the recent nuclear-magnetic-resonance experiments.